1 Answer
1

Since velocity dependent forces are not conservative, you cannot write them as the gradient of a potential function - ie. you cannot write a potential function as the integral of your non-conservative (dissipative) force. However, you can introduce a dissipative term into the equations and I believe it will work out from there. See, for example, http://www.phys.uri.edu/~gerhard/PHY520/mln9.pdf